Did you quote it correctly? It doesn't make sense the way it is written. Unless Fair is a name but then it should have been capitalized. You may have found a spelling mistake. it could be meant as promised fairly which would mean a reasonable and equal promise. As it is written it does not make sense.

That wording is not used currently (at least in American English). Here, "promised" means they seemed likely to be going to do something (grow up...). "Fair" is simply an intensifier. Thus, "promised fair" means that they seemed very likely to be going to do something. In other words, appearances indicated that it was very probable that they would grow up as rude savages.